Better Gap-Hamming lower bounds via better round elimination

Joshua Brody, Amit Chakrabarti, Oded Regev, Thomas Vidick, Ronald De Wolf

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Gap Hamming Distance is a well-studied problem in communication complexity, in which Alice and Bob have to decide whether the Hamming distance between their respective n-bit inputs is less than n/2 - √n or greater than n/2 + √n. We show that every k-round bounded-error communication protocol for this problem sends a message of at least Ω(n/(k 2logk)) bits. This lower bound has an exponentially better dependence on the number of rounds than the previous best bound, due to Brody and Chakrabarti. Our communication lower bound implies strong space lower bounds on algorithms for a number of data stream computations, such as approximating the number of distinct elements in a stream.

Original languageEnglish (US)
Title of host publicationApproximation, Randomization, and Combinatorial Optimization
Subtitle of host publicationAlgorithms and Techniques - 13th International Workshop, APPROX 2010 and 14th International Workshop, RANDOM 2010, Proceedings
Pages476-489
Number of pages14
DOIs
StatePublished - 2010
Event13th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2010 and 14th International Workshop on Randomization and Computation, RANDOM 2010 - Barcelona, Spain
Duration: Sep 1 2010Sep 3 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6302 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other13th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2010 and 14th International Workshop on Randomization and Computation, RANDOM 2010
CountrySpain
CityBarcelona
Period9/1/109/3/10

Keywords

  • Communication Complexity
  • Gap Hamming Distance
  • Measure Concentration
  • Round Elimination

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Fingerprint Dive into the research topics of 'Better Gap-Hamming lower bounds via better round elimination'. Together they form a unique fingerprint.

Cite this